Step |
Hyp |
Ref |
Expression |
1 |
|
simp1 |
|
2 |
|
psmetres2 |
|
3 |
2
|
3adant1 |
|
4 |
|
oveq2 |
|
5 |
4
|
imaeq2d |
|
6 |
5
|
cbvmptv |
|
7 |
6
|
rneqi |
|
8 |
7
|
metustfbas |
|
9 |
1 3 8
|
syl2anc |
|
10 |
|
fgval |
|
11 |
9 10
|
syl |
|
12 |
|
metuval |
|
13 |
3 12
|
syl |
|
14 |
|
fvex |
|
15 |
3
|
elfvexd |
|
16 |
15 15
|
xpexd |
|
17 |
|
restval |
|
18 |
14 16 17
|
sylancr |
|
19 |
|
inss2 |
|
20 |
|
sseq1 |
|
21 |
19 20
|
mpbiri |
|
22 |
|
vex |
|
23 |
22
|
elpw |
|
24 |
21 23
|
sylibr |
|
25 |
24
|
rexlimivw |
|
26 |
25
|
adantl |
|
27 |
|
nfv |
|
28 |
|
nfmpt1 |
|
29 |
28
|
nfrn |
|
30 |
29
|
nfcri |
|
31 |
27 30
|
nfan |
|
32 |
|
nfv |
|
33 |
31 32
|
nfan |
|
34 |
|
nfmpt1 |
|
35 |
34
|
nfrn |
|
36 |
|
nfcv |
|
37 |
35 36
|
nfin |
|
38 |
|
nfcv |
|
39 |
37 38
|
nfne |
|
40 |
|
simplr |
|
41 |
|
ineq1 |
|
42 |
41
|
adantl |
|
43 |
|
simp2 |
|
44 |
|
psmetf |
|
45 |
|
ffun |
|
46 |
|
respreima |
|
47 |
43 44 45 46
|
4syl |
|
48 |
47
|
ad6antr |
|
49 |
42 48
|
eqtr4d |
|
50 |
|
rspe |
|
51 |
40 49 50
|
syl2anc |
|
52 |
|
vex |
|
53 |
52
|
inex1 |
|
54 |
|
eqid |
|
55 |
54
|
elrnmpt |
|
56 |
53 55
|
ax-mp |
|
57 |
51 56
|
sylibr |
|
58 |
|
simpllr |
|
59 |
|
ssinss1 |
|
60 |
58 59
|
syl |
|
61 |
|
inss2 |
|
62 |
61
|
a1i |
|
63 |
|
pweq |
|
64 |
63
|
eleq2d |
|
65 |
53
|
elpw |
|
66 |
64 65
|
bitrdi |
|
67 |
|
ssin |
|
68 |
66 67
|
bitr4di |
|
69 |
68
|
ad5antlr |
|
70 |
60 62 69
|
mpbir2and |
|
71 |
|
inelcm |
|
72 |
57 70 71
|
syl2anc |
|
73 |
|
simplr |
|
74 |
|
eqid |
|
75 |
74
|
elrnmpt |
|
76 |
75
|
elv |
|
77 |
73 76
|
sylib |
|
78 |
33 39 72 77
|
r19.29af2 |
|
79 |
|
ssn0 |
|
80 |
79
|
ancoms |
|
81 |
80
|
3adant2 |
|
82 |
|
metuel |
|
83 |
81 43 82
|
syl2anc |
|
84 |
83
|
simplbda |
|
85 |
84
|
adantr |
|
86 |
78 85
|
r19.29a |
|
87 |
86
|
r19.29an |
|
88 |
26 87
|
jca |
|
89 |
|
simprl |
|
90 |
89
|
elpwid |
|
91 |
|
simpl3 |
|
92 |
|
xpss12 |
|
93 |
91 91 92
|
syl2anc |
|
94 |
90 93
|
sstrd |
|
95 |
|
difssd |
|
96 |
94 95
|
unssd |
|
97 |
|
simplr |
|
98 |
|
eqidd |
|
99 |
4
|
imaeq2d |
|
100 |
99
|
rspceeqv |
|
101 |
97 98 100
|
syl2anc |
|
102 |
43
|
ad4antr |
|
103 |
|
cnvexg |
|
104 |
|
imaexg |
|
105 |
74
|
elrnmpt |
|
106 |
102 103 104 105
|
4syl |
|
107 |
101 106
|
mpbird |
|
108 |
|
cnvimass |
|
109 |
108 44
|
fssdm |
|
110 |
102 109
|
syl |
|
111 |
|
ssdif0 |
|
112 |
110 111
|
sylib |
|
113 |
|
0ss |
|
114 |
112 113
|
eqsstrdi |
|
115 |
|
respreima |
|
116 |
102 44 45 115
|
4syl |
|
117 |
|
simpr |
|
118 |
|
simpllr |
|
119 |
118
|
elpwid |
|
120 |
117 119
|
eqsstrrd |
|
121 |
116 120
|
eqsstrrd |
|
122 |
114 121
|
unssd |
|
123 |
|
ssundif |
|
124 |
|
difcom |
|
125 |
|
difdif2 |
|
126 |
125
|
sseq1i |
|
127 |
123 124 126
|
3bitri |
|
128 |
122 127
|
sylibr |
|
129 |
|
sseq1 |
|
130 |
129
|
rspcev |
|
131 |
107 128 130
|
syl2anc |
|
132 |
|
elin |
|
133 |
6
|
elrnmpt |
|
134 |
133
|
elv |
|
135 |
134
|
anbi1i |
|
136 |
|
ancom |
|
137 |
132 135 136
|
3bitri |
|
138 |
137
|
exbii |
|
139 |
|
n0 |
|
140 |
|
df-rex |
|
141 |
138 139 140
|
3bitr4i |
|
142 |
141
|
biimpi |
|
143 |
142
|
ad2antll |
|
144 |
131 143
|
r19.29vva |
|
145 |
81
|
adantr |
|
146 |
43
|
adantr |
|
147 |
|
metuel |
|
148 |
145 146 147
|
syl2anc |
|
149 |
96 144 148
|
mpbir2and |
|
150 |
|
indir |
|
151 |
|
disjdifr |
|
152 |
151
|
uneq2i |
|
153 |
|
un0 |
|
154 |
150 152 153
|
3eqtri |
|
155 |
|
df-ss |
|
156 |
90 155
|
sylib |
|
157 |
154 156
|
eqtr2id |
|
158 |
|
ineq1 |
|
159 |
158
|
rspceeqv |
|
160 |
149 157 159
|
syl2anc |
|
161 |
88 160
|
impbida |
|
162 |
|
eqid |
|
163 |
162
|
elrnmpt |
|
164 |
163
|
elv |
|
165 |
|
pweq |
|
166 |
165
|
ineq2d |
|
167 |
166
|
neeq1d |
|
168 |
167
|
elrab |
|
169 |
161 164 168
|
3bitr4g |
|
170 |
169
|
eqrdv |
|
171 |
18 170
|
eqtrd |
|
172 |
11 13 171
|
3eqtr4rd |
|